Beam steering optics for near-eye and head mounted displays

ABSTRACT

A near-eye display system includes a display panel to present image frames to the eyes of a user for viewing. The system also includes a beam steering assembly facing the display panel that is configurable to displace a light beam incident on the beam steering assembly, thereby laterally shifting light relative to an optical path of the light beam incident on the beam steering assembly. The beam steering assembly includes a birefringent plate configurable to replicate a light ray incident on the beam steering assembly such that the replicated light ray is laterally shifted relative to an optical path of the light ray incident on the beam steering assembly.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application claims priority to U.S. patent application Ser.No. 15/889,796 (Attorney Docket No. 1500-G17033-US), entitled “BEAMSTEERING OPTICS FOR VIRTUAL REALITY SYSTEMS” and filed on Feb. 6, 2018,the entirety of which is incorporated by reference herein.

BACKGROUND

Head-mounted displays (HMDs) and other near-eye display systems canutilize an integral lightfield display, magnifier lens, lenslet orpinhole array, or other viewing opticts provide effective display ofthree-dimensional (3D) graphics. Generally, the integral lightfielddisplay employs one or more display panels and an array of lenslets,pinholes, or other optic features that overlie the one or more displaypanels. The HMDs and other near-eye display devices may have challengesassociated with the limited pixel density of current displays. Ofparticular issue in organic light emitting diode (OLED)-based displaysand other similar displays is the relatively low pixel fill factor; thatis, the relatively large degree of “black space” between pixels of theOLED-based displays. While this black space is normally undetectable fordisplays having viewing distances greater than arm's length from theuser, in HMDs and other near-eye displays this black space may bereadily detectable by the user due to the close proximity of the displayto the user's eyes. The visibility of the spacing between pixels (orsub-pixels) is often exacerbated due to magnification by the opticsoverlying the display panel. Therefore, there occurs a screen-dooreffect, in which a lattice resembling a mesh screen is visible in animage realized in the display, which typically interferes with userimmersion in the virtual reality (VR) or augmented reality (AR)experience.

BRIEF DESCRIPTION OF THE DRAWINGS

The present disclosure may be better understood, and its numerousfeatures and advantages made apparent to those skilled in the art byreferencing the accompanying drawings. The use of the same referencesymbols in different drawings indicates similar or identical items.

FIG. 1 is a diagram illustrating an arrangement of components of anear-eye display system utilizing a beam steering assembly to projectimagery in accordance with some embodiments.

FIG. 2 is a diagram illustrating a cross-section view of animplementation of the near-eye display system of FIG. 1 for providingsuper-resolution imagery in accordance with some embodiments.

FIG. 3 is a diagram illustrating a diffractive beam steering element foruse in the near-eye display system of FIG. 1 in accordance with someembodiments.

FIG. 4 is a diagram illustrating a refractive beam steering element foruse in the near-eye display system of FIG. 1 in accordance with someembodiments.

FIG. 5 a diagram illustrating another refractive beam steering elementfor use in the near-eye display system of FIG. 1 in accordance with someembodiments.

FIG. 6 is a flow diagram illustrating a method for sequential display ofimages to provide a super-resolution image display in the near-eyedisplay system of FIG. 1 in accordance with some embodiments.

FIG. 7 is a diagram illustrating a method of generating passivesuper-resolution images in accordance with some embodiments.

FIG. 8 is a diagram illustrating a top-down view of a birefringent beamsteering element in accordance with some embodiments.

FIG. 9 is a diagram illustrating a top-down view of another birefringentbeam steering element in accordance with some embodiments.

DETAILED DESCRIPTION

FIGS. 1-9 illustrate various systems and techniques for providingoptical beam steering in a near-eye display system or imaging system. Asdescribed in further detail below, a head mounted display (HMD) or othernear-eye display system implements a beam steering assembly disposedbetween a display panel and a user's eye. The beam steering assembly canbe deployed in a passive configuration to reduce or remove the screendoor effect or increase perceived resolution, or in an activeconfiguration (e.g. via time multiplexing) to increase effectiveresolution through exploitation of the visual persistence effects of thehuman eye. In some implementations, the near-eye display system projectstime-multiplexed images at a higher display rate such that two or moreof the images having different visual information are effectivelycombined by the human visual perception system into a single“super-resolution” image; that is, an image with an effective resolutionhigher than the native resolution of the display panel. In otherimplementations, the near-eye display system projects two or moreadjacent images having the same visual information but are spatiallyshifted via the beam steering apparatus relative to each other so as tobe perceived by the user as an image with light emitting elements ofincreased apparent size, and thus effectively covering the non-emissiveportions between the light emitting elements of the display.

FIG. 1 illustrates a near-eye display system 100 for implementation in ahead mounted device (HMD), heads-up display, or similar device inaccordance with some embodiments. As depicted, the near-eye displaysystem 100 includes a computational display sub-system 102. The near-eyedisplay system 100 further can include other components, such as aneye-tracking subsystem, an inertial measurement unit (IMU), audiocomponentry, and the like, that have been omitted for purposes ofclarity. The computational display sub-system 102 includes a left-eyedisplay 104 and a right-eye display 106 mounted in an apparatus 108(e.g., goggles, glasses, etc.) that places the displays 104, 106 infront of the left and right eyes, respectively, of the user.

As shown by view 110, each of the displays 104, 106 includes at leastone display panel 112 to display a sequence or succession of near-eyeimages, each of which comprises an array 114 of elemental images 116.The display panel 112 is used to display imagery to at least one eye 118of the user in the form of a normal image (e.g., for super-resolutionimplementations) or a lightfield (e.g., for lightfield implementations).In some embodiments, a separate display panel 112 is implemented foreach of the displays 104, 106, whereas in other embodiments the left-eyedisplay 104 and the right-eye display 106 share a single display panel112, with the left half of the display panel 112 used for the left-eyedisplay 104 and the right half of the display panel 112 used for theright-eye display 106.

As depicted, the near-eye display system 100 incudes a beam steeringassembly 120 overlying the display panel 112 so as to be disposedbetween the display panel 112 and the at least one eye 118 of a user.Cross view 122 depicts a cross-section view along line A-A of the beamsteering assembly 120 overlying the display panel 112. The beam steeringassembly 120 includes a stack of one or more optical beam steeringelements, such as the two optical beam steering elements 124, 126illustrated in FIG. 1, each optical beam steering element configured toreplicate and displace incident light rays originating from the displaypanel 112.

The near-eye display system 100 also includes a display controller 130to control the display panel 112 and, in some embodiments, a beamsteering controller 132 to control the operation of the beam steeringassembly 120. As also shown in FIG. 1, the near-eye display system 100also includes a rendering component 134 including a set of one or moreprocessors, such as the illustrated central processing unit (CPU) 136and graphics processing units (GPUs) 138, 140 and one or more storagecomponents, such as system memory 142, to store software programs orother executable instructions that are accessed and executed by theprocessors 136, 138, 140 so as to manipulate the one or more of theprocessors 136, 138, 140 to perform various tasks as described herein.Such software programs include, for example, rendering program 144comprising executable instructions for an optical beam steering andimage rendering process, as described below.

In operation, the rendering component 134 receives rendering information146 from a local or remote content source 148, where the renderinginformation 146 represents graphics data, video data, or other datarepresentative of an object or scene that is the subject of imagery tobe rendered and displayed at the display sub-system 102. Executing therendering program 144, the CPU 136 uses the rendering information 146 tosend drawing instructions to the GPUs 138, 140, which in turn utilizethe drawing instructions to render, in parallel, a series of imageframes 150 for display at the left-eye display 104 and a series oflightfield frames 152 for display at the right-eye display 106 using anyof a variety of well-known VR/AR computational/lightfield renderingprocesses.

As described in greater detail herein, the beam steering assembly 120laterally displaces, or “shifts” the position of pixels in the imageframes 150, 152 to fill in non-emissive portions of the display panel112. For example, in some embodiments, the beam steering assembly 120shifts the position of successive images displayed at the display panel112 so as to project to the user a super-resolution image or ahigher-resolution lightfield due to the succession of images effectivelybeing superimposed due to the visual persistence effect of the humanvisual system. In other embodiments, the beam steering assembly 120replicates pixels of each given image and laterally displaces thereplicated pixels so as to project an image with pixels of a perceivedlarger size (e.g., due to increased effective pixel count) that concealsthe non-emissive space between pixels. It will be appreciated thatalthough described in the context of the near-eye display system 100,the beam steering described herein may be used for any type of VR or ARsystem (e.g., conventional magnifier displays, computational displays,see-through displays, and the like).

FIG. 2 illustrates a cross-section view of an implementation 200 of thenear-eye display system 100 for providing super-resolution imagery tothe eye 118 of the user in accordance with at least one embodiment ofthe present disclosure. In this example, the display panel 112 comprisesan array of pixels, which typically are arranged as an interwovenpattern of sub-pixels of different colors, such as red, green, and blue(RGB) sub-pixels, and wherein the spatial persistence effects of humanvision result in adjacent sub-pixels of different colors to be perceivedas a single pixel having a color represented by a blend of the adjacentsub-pixels and their respective intensities. For ease of illustration,the display panel 112 is not depicted to scale, and is depicted ashaving only five sub-pixels in the cross-section (sub-pixels 202, 204,206, 208, 210), whereas a typical display would have hundreds orthousands of sub-pixels along the cross-section, and thus it will beappreciated that the dimensions of the sub-pixels 202-210, and thenon-emissive space in between the sub-pixels (e.g., non-emissive space212 between sub-pixels 206 and 208) is significantly exaggeratedrelative to the other components of the implementation 200.

Further, to aid in illustration of the operation of the beam steeringassembly 120, the implementation 200 of FIG. 2 illustrates the beamsteering assembly 120 as having only a single optical beam steeringelement 214. Moreover, in FIG. 2, the user's eye 118 is depicted as alens 216 representing the lens of the eye 118 and a panel 218representing the retinal plane of the eye 118. As such, the panel 218 isalso referred to herein as “retina 218.” Further, the implementation 200includes a magnifier lens assembly 220 (not shown in FIG. 1 for ease ofillustration) overlaying the display panel 112 such as to be disposedbetween the optical beam steering element 214 and the eye 118 of theuser. Although illustrated in FIG. 2 to be a single lens, in otherembodiments, the magnifier lens assembly 220 includes a lenslet array(not shown) with each lenslet focusing a corresponding region of thedisplay panel 112 onto the lens 216 of the eye. It also should be notedthat while FIG. 2 depicts an optical configuration with a single lensand the optical beam steering element 214 between the display panel 112and the eye 118, in a typical implementation the optical system maycomprise a larger number of lenses, prisms, or other optical elementsbetween the display panel 112 and the eye 118.

As shown, the optical beam steering element 214 is configured toreplicate light originating from sub-pixel 206 and displace thereplicated sub-pixel such that the eye 118 perceives the replicatedsub-pixel as originating from the non-emissive space 212 betweensub-pixels 206 and 208, and thus create a perception of a display havingan effective resolution of approximately twice the actual resolution ofthe display panel 112. To illustrate, in one embodiment, the beamsteering controller 132 of FIG. 1 at time to deactivates the beamsteering element 214 and the display controller 130 scans in a firstimage for display by the display panel 112. The resulting light outputby sub-pixel 206 for the first image is directed to adisplay-panel-facing surface of the beam steering element 214. Becausethe beam steering element 214 is deactivated at time to, the incidentlight is passed through the beam steering element 214 without lateraldisplacement to the user's eye 118, whereupon the lens 216 of the eye118 focuses the light on the retina 218 at position 222 (with light fromthe other sub-pixels 202-204 and 208-210 taking corresponding paths).

Subsequently, at time ti, the beam steering controller 132 of FIG. 1activates the beam steering element 214, which configures the beamsteering element 214 to laterally displace incident light (e.g.,two-dimensional shift of incident light in the X- and/or Y-axisdirections of FIG. 2). The display controller 130 scans in a secondimage for display by the display panel, and the resulting light outputby sub-pixel 206 for the second image is directed to thedisplay-panel-facing surface of the beam steering element 214. Becausethe beam steering element 214 is activated at time ti, the incidentlight is laterally displaced after passing through the beam steeringelement 214. The laterally-displaced light is passed to the user's eye118, whereupon the lens 216 of the eye 118 focuses the light on theretina 218 at position 224. The eye 118 perceives light at position 224as originating from the non-emissive space 212 between sub-pixels 206and 208 (although the light actually originated from sub-pixel 206). Thelateral displacement of incident light at the beam steering element 214results in presenting sub-pixels of the second image at positions wherenon-emissive spaces would have been perceived as black space by the eye118 from the display of the first image at time to. Thus, if the firstimage at time to and the second image at time ti are displayed in quicksuccession (i.e., within the visual persistence interval of the humaneye, which is approximately 10 ms), the human visual system perceivesthe first and second images to be overlapping. That is, in this example,the lateral displacement introduced to the light of the second image hasthe result of presenting the sub-pixels of the second image where blackspaces would have appeared to the eye 118 from the display of the firstimage, and thus the sub-pixels of the second image appear to the eye 118to occupy black spaces associated with non-emissive portions of thedisplay panel 112 for the first image.

The second image at time ti, in some embodiments, has the same visualcontent as the first image at time to. In such embodiments, the eye 118perceives the two images as overlapping in a single image of the sameresolution of the first and second images (i.e., at native resolution ofthe display panel 112) but with larger perceived pixels that fill in theblack space associated with non-emissive portions of the display panel112, and thus reduce or eliminate the screen-door effect that wouldotherwise be visible to the eye 118. In other embodiments, the secondimage at time ti has different visual content than the first image attime to. In such embodiments, the eye 118 perceives the two images asoverlapping in a single super-resolution image with visual content ofthe second image filling in the black space associated with non-emissiveportions of the display panel 112. This reduces or eliminates the user'sability to perceive these non-emissive portions of the display panel112, thereby creating a perception of a display having an effectiveresolution of approximately twice the actual resolution of the displaypanel 112.

It should be noted that although the implementation 200 of the near-eyedisplay system 100 in FIG. 2 depicts a beam steering assembly having asingle beam steering element 214 for lateral light displacement, asnoted above the beam steering assembly 120 may employ a stack ofmultiple beam steering elements (e.g., beam steering elements 124, 126of FIG. 1) of differing configurations so as to provide multipledifferent lateral displacements, and thus provide the option to shiftmultiple successive images in different directions. For example,assuming the stack uses beam steering elements having a replicationfactor of two (e.g., beam steering element 214 of FIG. 2 that passesincident light to two different locations as either laterally displacedor not laterally displaced based on two corresponding states of the beamsteering element 214, activated or deactivated), a stack of four beamsteering elements allows for the replication and steering of eachsub-pixel of the display panel to four different positions (i.e., threelaterally displaced positions plus one original sub-pixel position inwhich all four beam steering elements are deactivated so that lightpasses through without any lateral displacement).

It should further be noted that although the example of FIG. 2 isdescribed in the context of a beam steering element 214 having areplication factor of two (i.e., deactivated to pass through without anylateral displacement or activated to replicate a sub-pixel for shiftingto another position), other embodiments may employ beam steeringelements having multiple different states. For example, instead of usinga stack of four beam steering elements that each have a replicationfactor of two, a single beam steering element (not shown) having areplication factor of four may be controlled by beam steering controller132 of FIG. 1 to switch between four different states that allow for thereplication and steering of each sub-pixel of the display panel to fourdifferent positions (i.e., three laterally displaced positions plus oneoriginal sub-pixel position in which all four beam steering elements aredeactivated so that light passes through without any lateraldisplacement).

In some embodiments, an amount of screen door effect perception (i.e.,metric of screen door effect severity) is represented by the equation:MTF(u)*CSF(u) for all spatial frequencies u, where MTF represents aModulation Transfer Function specifying how different spatialfrequencies are handled by the optics of a system (e.g., the near-eyedisplay system 100) and CSF represents a Contrast Sensitivity Functionrepresenting the eye's ability to discern between luminances ofdifferent levels in a static image. The product of eye's contrastsensitivity (i.e., how sensitive the eye is to certain spatialfrequencies, which turns out to be very sensitive to screen doorfrequency) and the spatial frequency content of pattern produced withreplication provides a system transfer function in which the larger thetransfer function is (for that specific spatial frequency u), the morescreen door will be perceived. Accordingly, reduction of the systemtransfer function can be represented by an optimization metric asprovided by equation (1) below:

$\begin{matrix}{\min\limits_{d,\theta}\frac{\int_{u_{\min}}^{u_{\max}}{{{PTF}\left( {u,d,\theta} \right)}{{CSF}(u)}{du}}}{\int_{u_{\min}}^{u_{\max}}{{{PTF}\left( {u,0,0} \right)}{{CSF}(u)}{du}}}} & (1)\end{matrix}$

where u represents spatial frequency, d represents possible lateraldisplacement between replication spots, and 0 represents rotation ofreplication/beam steering elements. The product of the equation providesa metric of how much screen door effect is perceivable after stacking anumber N of beam steering elements. For example, based on equation (1)for a beam steering element (which can also be referred to as a“filter”) having a replication factor of two (such as described hereinwith respect to FIG. 2), one filter results in approximately 41%perceptibility of the screen door effect, two filters results inapproximately 14% perceptibility of the screen door effect, threefilters results in approximately 7.5% perceptibility of the screen dooreffect, and four filters results in approximately 3.1% perceptibility ofthe screen door effect. Accordingly, increasing the number of beamsteering elements in a stack for the beam steering assembly generallyreduces perceptibility of the screen door effect.

The beam steering assembly is implementable using any of a variety ofsuitable optical beam steering elements capable of sub-pixel-scalesteering (i.e., steer replicated sub-pixels between positions based onstates of the beam steering element). For example, FIG. 3 is a diagramillustrating a diffractive beam steering element in accordance with someembodiments. In the example of FIG. 3, a beam steering element 300(e.g., one of the beam steering elements 124, 126 of FIG. 1 or beamsteering element 214 of FIG. 2) is a stacked pair of gratings includinga first grating 302 and a second grating 304 that splits and diffractsincident light into several beams traveling in different directions.

In some embodiments, the relationship between grating spacing and theangles of the incident and diffracted beams of light for beam steeringelement 300 is represented by equations (2) and (3):

$\begin{matrix}{{\theta = {\sin^{- 1}\frac{n\; \lambda}{D}}},} & (2) \\{{t = \frac{d}{\tan \mspace{14mu} \theta}},} & (3)\end{matrix}$

where θ represents the diffractive angle between beams of diffractedlight (i.e., angular deflection of the diffracted beam, n represents theorder number, λ represents the wavelength of incident light, Drepresents the period of the gratings, t represents the distance betweenthe gratings, and d represents the optical lateral displacement betweenthe replicated sub-pixels. As discussed in more detail relative to FIG.2, the lateral displacement distance d is less than a pixel to fill inthe non-emissive portions between sub-pixels.

As shown, the first grating 302 of beam steering element 300 diffractsan incident beam of light 306 (e.g., light from a sub-pixel of thedisplay panel) into the ±1 first orders. The second grating 304 of thegrating pair further diffracts the light beams of ±1 first orders intothe the ±2 second orders and reverses the angular deflection of thediffracted beams such that light beams passing through the secondgrating 304 (and therefore leaving the beam steering element 300) has adirection matching the incidence angle of the incident beam of light 306from sub-pixels of the display panel. In this manner, the beam steeringelement 300 replicates the original incident beam of light 306 andlaterally displaces the replicated beams. Various amplitude or phasegratings may be utilized for diffracting the incident light beam andthen reversing the angular deflection without departing from the scopeof this disclosure. Further, the gratings may be designed for single ormultiple diffraction orders to reduce thickness of the beam steeringelement.

In some embodiments, the relative spot intensities (i.e. diffractionefficiency) of spots (e.g., replicated beams of light) replicated bybeam steering element 300 is represented by equation (4):

sin c(n*w/D)²   (4)

where n represents diffraction order number, w/D is the open fraction ofthe grating, and sin c(x)=sin(π*x)/(π*x). Accordingly, the intensity ofthe replicated spots may be adjusted based on the open fraction ofgratings in beam steering element 300.

In another embodiment, FIG. 4 is a diagram illustrating a refractivebeam steering element in accordance with some embodiments. In theexample of FIG. 4, a beam steering element 400 (e.g., one of the beamsteering elements 124, 126 of FIG. 1 or beam steering element 214 ofFIG. 2) is a stacked pair of prisms including a first prism 402 and asecond prism 404 that refracts incident light into several beamstraveling in different directions. As shown, the first prism 402angularly disperses an incident beam of white light 406 from the displaypanel 112 into three angularly-deviated rays. As the refractive index ofprisms varies with the wavelength (i.e., color) of light, rays ofdifferent colors will be refracted differently and leave the first prism402, thereby separating the incident beam of white light 406 into red,green, and blue rays. The red ray R has a longer wavelength than thegreen ray G and the blue ray B, and therefore leaves the first prism 402with less angular deviation relative to the incident beam of white light406 than the other rays. Similarly, the green ray G has a longerwavelength than the blue ray B, and therefore leaves the first prism 402with less angular deviation relative to the incident beam of white light406 than the blue ray B.

As shown, the second prism 404 receives the three angularly-deviatedrays from the first prism 402 and reverses the angular deviations suchthat the rays leaving the second prism 404 (and therefore leaving thebeam steering element 400) have red, green, and blue colored raysdisplaced laterally while having a direction matching the incidenceangle of the incident beam of white light 406. In this manner, the beamsteering element 400 spreads out or changes the location of pixels at asub-pixel scale.

FIG. 5 a diagram illustrating another refractive beam steering elementin accordance with some embodiments. In the example of FIG. 5, a beamsteering element 500 (e.g., one of the beam steering elements 124, 126of FIG. 1 or beam steering element 214 of FIG. 2) includes a liquidcrystal cell 502 having liquid crystal molecules 504 oriented such as toform a birefringent material having a refractive index that depends onthe polarization and propagation direction of light. As shown, theliquid crystal molecules 504 are oriented to have their symmetry axes at45 degrees relative to the substrate plane. Accordingly, due to thedouble refraction phenomenon whereby a ray of incident light is splitbased on polarization into two rays taking slightly different paths, anincident beam of unpolarized light 506 is split into two rays 508, 510and steered to one of two deflection angles, depending on polarizationstate.

For the incident beam of unpolarized light 506, a first ray 508 having afirst polarization state (e.g., light whose polarization isperpendicular to the optic axis of the liquid crystal cell 502, referredto as “ordinary axis oriented”) passes through the liquid crystal cell502 without deflection. The second ray 510 having a second polarizationstate (e.g., light whose polarization is in the direction of the opticaxis of the liquid crystal cell 502, referred to as “extraordinary axisoriented”) is deflected and is passed with a lateral displacement d.

In some embodiments, the beam steering element 500 includes liquidcrystal molecules 504 that are oriented as illustrated in FIG. 5 andpolymerized such that the liquid crystal molecules 504 are linked to bestatic in that configuration, thereby forming a beam replicationassembly. In other embodiments, the beam steering element 500 furtherincludes a polarization switch (not shown) stacked on top of thepolymerized liquid crystal cell that switches polarization between twovalues so that the liquid crystal molecules 504 only received polarizedlight (rather than the beam of unpolarized light 506 illustrated in FIG.5). Accordingly, depending on the polarization of incident light, theincoming polarized light is either passed through or deviated (ratherthan passing both rays 508, 510 as illustrated in FIG. 5).

It should be noted that while embodiments implementing various beamsteering elements (such as the beam steering elements of FIGS. 3-5 and8-9) are described herein for illustrative purposes, other suitable beamsteering elements capable of lateral (i.e., not angular) sub-pixelshifts may be implemented in place of the beam steering elementsdescribed herein unless otherwise noted.

FIG. 6 illustrates an example method 600 of operation of the near-eyedisplay system 100 for display of super-resolution imagery in accordancewith various embodiments. As described above relative to FIGS. 1-2, thenear-eye display system 100 takes advantage of the visual persistenceeffect to provide a time-multiplex display of shifted imagery so thateither a series of images is perceived by the user as either a singlesuper-resolution image or a native-resolution image with effectivelylarger pixels that conceal the non-emissive portions of the displaypanel 112. The method 600 illustrates one iteration of the process forrendering and displaying an image for one of the left-eye display 104 orright-eye display 106, and thus the illustrated process is repeatedlyperformed in parallel for each of the displays 104, 106 to generate anddisplay a different stream or sequence of frames for each eye atdifferent points in time, and thus provide a 3D, autostereoscopic VR orAR experience to the user.

The method 600 initiates at block 602 with determining a display imageto be generated and displayed at the display panel 112. In someembodiments, the rendering component 134 identifies the image content tobe displayed to the corresponding eye of the user as a frame. In atleast one embodiment, the rendering component 134 receives pose datafrom various pose-related sensors, such as a gyroscope, accelerometer,magnetometer, Global Positioning System (GPS) sensor, and the like todetermines a current pose of the apparatus 108 (e.g., HMD) used to mountthe displays 104, 106 near the user's eyes. From this pose data, the CPU136, executing the rendering program 144, can determine a correspondingcurrent viewpoint of the subject scene or object, and from thisviewpoint and graphical and spatial descriptions of the scene or objectprovided as rendering information 146, determine the imagery to berendered.

At block 604, the rendering program 144 manipulates the CPU 136 tosample the source image and generate a first array of pixelsrepresenting imagery to be rendered (e.g., as determined in block 602).The generated first array of pixels is subsequently transmitted to thedisplay panel 112 to be displayed.

At block 606, the beam steering controller 132 configures the beamsteering assembly 120 to be in a first configuration state while thedisplay controller 130 controls the display panel 112 facing the beamsteering assembly 120 to display the first array of pixels generated inblock 604. In some embodiments, such as described above relative to timeto in FIG. 2, the first configuration state of the beam steeringassembly is a deactivated state in which the optical beam steeringelement 214 allows the first array of pixels to be passed without anylateral displacements. In other embodiments, the first configurationstate of the beam steering assembly laterally displaces the first arrayof pixels such that they are not laterally aligned with the originaloptical path between the display panel 112 and the beam steeringassembly 120. Accordingly, the beam steering assembly, while in thefirst configuration state, imparts a first lateral displacement to thefirst array of pixels.

As explained above, for various beam steering devices, the switchingbetween configuration states for the beam steering assembly typicallyincludes activating or deactivating a particular combination of stagesof the stack of beam steering elements comprising the beam steeringassembly, such that the array of pixels leaving the beam steeringassembly is laterally shifted based on the configuration state. Notethat the process of block 606 may be performed concurrently with thecorresponding image generation at block 604.

At block 608, the rendering program 144 manipulates the CPU 136 tosample the source image and generate a second array of pixelsrepresenting imagery to be rendered (e.g., as determined in block 602).The generated second array of pixels is subsequently transmitted to thedisplay panel 112 to be displayed.

At block 610, the beam steering controller 132 configures the beamsteering assembly 120 to be in a second configuration state while thedisplay controller 130 controls the display panel 112 facing the beamsteering assembly 120 to display the second array of pixels generated inblock 608. In some embodiments, such as described above relative to timeti in FIG. 2, the second configuration state of the beam steeringassembly is an activated state in which the optical beam steeringelement 214 laterally displaces the second array of pixels such thatthey are not laterally aligned with first array of pixels.

As explained above, for various beam steering devices, the switchingbetween configuration states for the beam steering assembly typicallyincludes activating or deactivating a particular combination of stagesof the stack of beam steering elements comprising the beam steeringassembly, such that the array of pixels leaving the beam steeringassembly is laterally shifted based on the configuration state. Notethat the process of block 608 may be performed concurrently with thecorresponding image generation at block 610.

At block 612, the display controller 130 instructs the display panel todisplay the first and second array of pixels (e.g., as generated fromblocks 604-610) within a visual perception interval so that the firstand second first and second array of pixels are perceived by a user tobe a single image with an effective resolution that is higher than anative resolution of the display panel 112, thereby presenting asuper-resolution image.

It should be noted that although the method 600 of FIG. 6 is describedin the context of only combining two arrays of pixels that are laterallyshifted to each other to generate a super-resolution image, thoseskilled in the art will recognize that the number and rate of iterationsof the processes of blocks 604-610 may be varied increase the number oflaterally shifted images to be displayed by display panel 112 during thevisual persistence interval of the human eye. For example, assuming thebeam steering assembly 120 includes a stack of multiple different beamsteering elements (e.g., beam steering elements 124, 126 of FIG. 1) withdifferent configuration states, the processes of blocks 604-608 arerepeated for each of the different configuration states so that multiplearrays of pixels that are laterally shifted relative to each other maybe generated and displayed so as to be perceived as a singlesuper-resolution image by the user. Alternatively, rather thanresampling the source image between each lateral displacement of pixels,the same array of pixels can be shifted across the various configurationstates and displayed so as to be perceived as a singlestandard-resolution image with reduced screen-door effect by the user.

As demonstrated above, the various optical beam steering assembliesdescribed may be advantageously used to leverage the visual persistenceeffect of the human visual system to provide dynamicallytime-multiplexed, spatially shifted images that are perceived by a useras super-resolution images or native-resolution images with reducedperception of non-emissive portions of the display. Additionally, inother embodiments, the optical beam steering assemblies described may beused to passively replicate (i.e., without sending control voltages andchanging states of the beam steering assemblies) and spatially shiftincident light beams coming from the display panel to providenative-resolution images with reduced perception of non-emissiveportions of the display.

It will be appreciated that other embodiments provide for passivesuper-resolution without any time-multiplexing of images. FIG. 7 is adiagram illustrating a method of generating passive super-resolutionimages in accordance with some embodiments. As shown, a first image 702includes a plurality of pixels (with only four pixels 704, 706, 708, 710shown for ease of illustration). A second image 712 provides the samecontent data (e.g., pixels 704, 706, 708, 710) as the first image 702,but is laterally shifted in position relative to the first image 702.

For example, in some embodiments, the first image 702 and the secondimage 712 are generated by presenting unpolarized light from a displayscreen to the beam steering element 500 of FIG. 5. For the incidentunpolarized light, a first set of light rays having a first polarizationstate (e.g., light whose polarization is perpendicular to the optic axisof the beam steering element 500) passes through without deflection,thereby providing the first image 702. Additionally, for the sameincident unpolarized light, a second set of light rays having a secondpolarization state (e.g., light whose polarization is in the directionof the optic axis of the beam steering element 500) is deflected andpassed through with a lateral displacement d of a sub-pixel distance. Inthis example, the lateral displacement d is half a pixel in the x-axisdirection and half a pixel in the y-axis direction, thereby diagonallyshifting each of the pixels by half a pixel for the second image 712.

The first image 702 is overlaid with one or more sub-pixel shiftedcopies of itself (e.g., the second image 712) to generate a summed image714 which is perceivable as having improved resolution relative to thatof the first image 702 and the second image 712. It will be appreciatedthat depending on the overlap, certain sub-pixel portions of the summedimage 714 gets contributions from the same pixel value. For example, thesub-pixel portion 716 provides image data that is provided only by thevalue of pixel 704. Other sub-pixel portions of the summed image 714gets contributions from multiple different pixel values. For example,the sub-pixel portion 716 provides image data that is provided by boththe values of pixel 704 and pixel 706. In this manner, the effectiveresolution of the perceived image (i.e., summed image 714) is increasedwithout requiring time-multiplexing of images or coordinating therendering of images with varying the states of beam steering elements.

FIG. 8 is a diagram illustrating a top-down view of a birefringent beamsteering element in accordance with some embodiments. In the example ofFIG. 8, the beam steering element 800 (e.g., one of the beam steeringelements 124, 126 of FIG. 1 or beam steering element 214 of FIG. 2) is alayer of birefringent material that is tilted relative to a planar axis802. As defined herein, the planar axis 802 represents a longitudinalaxis along which the beam steering element 800 would be oriented if thebeam steering element were parallel to the display panel 112.

In some embodiments, the layer of birefringent material of the beamsteering element 800 is a birefringent plate 800 including a stretchedpolymer plate. Many polymers have a polarizability anisotropy or areinherently isotropic due to their three-dimensional chemical structures,and as such do not show birefringence in an unstressed state. In acompletely amorphous state, polarizability anisotropies for repeatingunits are compensated by each other because the polymer molecular chainsare randomly oriented. As a result, the polymer macroscopically becomesoptically isotropic and exhibits no birefringence. The polymer, however,exhibits birefringence when the polymer molecular chains are oriented bystress. For example, when the polymer is subjected to stresses fromextrusion, stretching and injection, blow molding processes, or postmanufacturing unintentional damage, the induced stress shows up asbirefringence in the finished materials.

It should be noted that while embodiments implementing various beamsteering elements as stretched polymer plates or stretched polymer filmsare described herein for illustrative purposes, other suitablebirefringent beam steering elements capable of lateral (i.e., notangular) sub-pixel shifts may be implemented in place of the beamsteering elements described herein unless otherwise noted. For example,various birefringent materials formed from stress and strain due toexternal forces and/or deformation acting on materials that are notnaturally birefringent, such as deformed glass, plastic lenses, andstressed polymer castings, may be used without departing from the scopeof this disclosure. Additionally, in other embodiments, the

As shown in FIG. 8, the birefringent plate 800 includes an in-planesymmetry axis 804 that is parallel to the longitudinal length of thebirefringent plate 800. For each input ray of light 806, thebirefringent plate 800 generates two output rays of light 808, 810 byreplicating the input ray of light 806. Thus, both of the replicatedrays of light (i.e., output rays of light 808, 810) represent the samevisual content as the input ray of light 806 incident on the beamsteering assembly. One of the output rays of light 808 is passed throughthe birefringent plate 800 along substantially the same direction as anoptical path 812 of the incident, input ray of light 806 (i.e., thelight ray incident on the beam steering assembly). The other output rayof light 810 is a replicated ray of the incident, input ray of light 806that is laterally displaced (e.g., two-dimensional shift of incidentlight in the X- and/or Y-axis directions of FIG. 8) relative to theinput ray of light 806 and the output ray of light 808. It should benoted that the birefringent plate 800 causes lateral ray displacementbut does not cause angular displacement of light rays. That is, a lightray emitted from the display panel 112 does not undergo a change in theangular direction of its light path (i.e., the optical path of the lightbeam incident on the beam steering element 800). Thus, the beam steeringelement (i.e., birefringent plate 800) replicates pixels of each givenimage and laterally displaces the replicated pixels so as to project animage with pixels of a perceived larger size (e.g., due to increasedeffective pixel count) that conceals the non-emissive space of displaypanel 112 between pixels.

In some embodiments, the beam steering element 800 is coupled to anactuator 814 configured to rotate the beam steering element 800 aroundthe X-axis, Y-axis, and/or Z-axis such as to change the relative anglebetween the in-plane symmetry axis 804 of the birefringent plate and theplanar axis 802. In various embodiments, the actuator 814 is controlledby the rendering component 134 to change the amount of lateraldisplacement between the two output rays of light 808, 810. In variousembodiments, the actuator 814 may include optomechanical actuators suchas piezo-electric, voice-coil, or electro-active polymer actuators.Although described here in the context of optomechanical actuators,those skilled in the art will recognize that any mechanical actuatorcapable of physically rotating the beam steering element 800 may be usedwithout departing from the scope of this disclosure.

In various embodiments, a distance Δx by which a replicated ray islaterally displaced is represented by the following equations:

$\begin{matrix}{{\Delta \; x} = {\alpha*\Delta \; z}} & (5) \\{\alpha = {\theta - {\arctan \left( {\frac{n_{o}^{2}}{n_{e}^{2}}\tan \mspace{14mu} \theta} \right)}}} & (6)\end{matrix}$

where Δz is the thickness of the birefringent plate 800 and a is theangular deviation of the replicated ray inside the birefringent plate800, which after exiting turns into a lateral displacement of Δx. θrepresents a tilt angle between the in-plane symmetry axis 804 of thebirefringent plate and the angle of the incoming input ray of light 806incident on the beam steering assembly (or the planar axis 802).Generally, a distance of max displacement is achieved when the in-planesymmetry axis 804 of the birefringent plate is at 45 degrees relative tothe incoming ray. At 90 degrees, zero displacement of the replicated rayoccurs.

It should be noted that although the example of FIG. 8 is described inthe context of a beam steering element 800 having a replication factorof two (i.e., replicate an incoming input ray and sub-pixel lateralshifting to another position), other embodiments may employ a stack ofbirefringent plate beam steering elements to increase the amount of raymultiplication. For example, as described below in more detail relativeto FIG. 9, instead of using a single tilted birefringent plate, by usinga stack of two tilted birefringent plates that each have a replicationfactor of two, a single beam steering element having a replicationfactor of four may be controlled by beam steering controller 132 and/orthe rendering component 134 of FIG. 1 to allow for the replication andsteering of each sub-pixel of the display panel to four differentpositions (i.e., three laterally displaced positions plus one originalsub-pixel position).

FIG. 9 is a diagram illustrating a top-down view of another birefringentbeam steering element in accordance with some embodiments. In theexample of FIG. 9, the beam steering element 900 (e.g., one of the beamsteering elements 124, 126 of FIG. 1 or beam steering element 214 ofFIG. 2) is tilted relative to the planar axis 902 and includes a stackof birefringent plates including a first birefringent plate 904 and asecond birefringent plate 906. Similar to that of FIG. 8, the planaraxis 902 represents a longitudinal axis along which the beam steeringelement 900 would oriented if the beam steering element were parallel tothe display panel 112. The beam steering element 900 further includes aquarter wave plate 908 positioned between the first birefringent plate904 and the second birefringent plate 906.

In various embodiments, each layer of birefringent material of the beamsteering element 900 (e.g., the first birefringent plate 904 and thesecond birefringent plate 906) is a stretched polymer plate. However,while embodiments implementing various beam steering elements asstretched polymer plates or stretched polymer films are described hereinfor illustrative purposes, other suitable birefringent polymer beamsteering elements capable of lateral (i.e., not angular) sub-pixelshifts may be implemented in place of the beam steering elementsdescribed herein unless otherwise noted. For example, variousbirefringent materials formed from stress and strain due to externalforces and/or deformation acting on materials that are not naturallybirefringent, such as deformed glass, plastic lenses, and stressedpolymer castings, may be used without departing from the scope of thisdisclosure.

As shown in FIG. 9, the first birefringent plate 904 includes anin-plane symmetry axis 910 that is parallel to the longitudinal lengthof the first birefringent plate 904. For each input ray of light 914,the first birefringent plate 904 generates two output rays of light (notshown). One of the output rays of light is passed through the firstbirefringent plate 904 along substantially the same direction as anoptical path of the incident, input ray of light 914. The other outputray of light is a replicated ray of the incident, input ray of light 914that is laterally displaced (e.g., two-dimensional shift of incidentlight in the X- and/or Y-axis directions of FIG. 9) relative to theinput ray of light 914. Thus, both of the replicated rays of light(i.e., output rays of light output from the first birefringent plate904) represent the same visual content as the input ray of light 914incident on the beam steering assembly. The quarter wave plate 908polarizes those two output rays of light (i.e., replicated raysresulting from the input ray of light 914 passing through the firstbirefringent plate 904) to generate light rays having circularpolarization prior to the light rays reaching the second birefringentplate 906. If light incident on the birefringent plates is notcircularly polarized, spot multiplication (i.e., light ray replication)does not occur.

For each input ray of light, the second birefringent plate 906 alsogenerates two output rays of light (not shown). Accordingly, thepolarized two output rays of light (i.e., replicated rays resulting fromthe input ray of light 914 passing through the first birefringent plate904 and the quarter wave plate 908) result in a total of at least fouroutput rays of light 916. Thus, the replicated rays of light (i.e.,output rays of light 916) represent the same visual content as the inputray of light 914 incident on the beam steering assembly. One of theoutput rays of light 916 is passed through the beam steering element 900along substantially the same direction as an optical path of theincident, input ray of light 914 (i.e., the light ray incident on thebeam steering assembly). The other three output rays of light 916 arelaterally displaced relative to the optical path. In this manner, thebeam steering element 900 replicates pixels of each given image andlaterally displaces the replicated pixels so as to project an image withpixels of a perceived larger size (e.g., due to increased effectivepixel count) that conceals the non-emissive space of display panel 112between pixels.

In some embodiments, the beam steering element 900 is coupled to anactuator 918 configured to rotate the beam steering element 900 aroundthe X-axis, Y-axis, and/or Z-axis such as to change the relative anglebetween the in-plane symmetry axes 910, 912 of the beam steering element900 and the planar axis 902. In various embodiments, the actuator 918 iscontrolled by the rendering component 134 to change the amount oflateral displacement between the four output rays of light 916. Invarious embodiments, the actuator 918 may include optomechanicalactuators such as piezo-electric, voice-coil, or electro-active polymeractuators. Although described here in the context of optomechanicalactuators, those skilled in the art will recognize that any mechanicalactuator capable of physically rotating the beam steering element 900may be used without departing from the scope of this disclosure.

In some embodiments, certain aspects of the techniques described abovemay implemented by one or more processors of a processing systemexecuting software. The software comprises one or more sets ofexecutable instructions stored or otherwise tangibly embodied on anon-transitory computer readable storage medium. The software caninclude the instructions and certain data that, when executed by the oneor more processors, manipulate the one or more processors to perform oneor more aspects of the techniques described above. The non-transitorycomputer readable storage medium can include, for example, a magnetic oroptical disk storage device, solid state storage devices such as Flashmemory, a cache, random access memory (RAM) or other non-volatile memorydevice or devices, and the like. The executable instructions stored onthe non-transitory computer readable storage medium may be in sourcecode, assembly language code, object code, or other instruction formatthat is interpreted or otherwise executable by one or more processors.

A computer readable storage medium may include any storage medium, orcombination of storage media, accessible by a computer system during useto provide instructions and/or data to the computer system. Such storagemedia can include, but is not limited to, optical media (e.g., compactdisc (CD), digital versatile disc (DVD), Blu-Ray disc), magnetic media(e.g., floppy disc, magnetic tape, or magnetic hard drive), volatilememory (e.g., random access memory (RAM) or cache), non-volatile memory(e.g., read-only memory (ROM) or Flash memory), ormicroelectromechanical systems (MEMS)-based storage media. The computerreadable storage medium may be embedded in the computing system (e.g.,system RAM or ROM), fixedly attached to the computing system (e.g., amagnetic hard drive), removably attached to the computing system (e.g.,an optical disc or Universal Serial Bus (USB)-based Flash memory), orcoupled to the computer system via a wired or wireless network (e.g.,network accessible storage (NAS)).

Note that not all of the activities or elements described above in thegeneral description are required, that a portion of a specific activityor device may not be required, and that one or more further activitiesmay be performed, or elements included, in addition to those described.Still further, the order in which activities are listed are notnecessarily the order in which they are performed. Also, the conceptshave been described with reference to specific embodiments. However, oneof ordinary skill in the art appreciates that various modifications andchanges can be made without departing from the scope of the presentdisclosure as set forth in the claims below. Accordingly, thespecification and figures are to be regarded in an illustrative ratherthan a restrictive sense, and all such modifications are intended to beincluded within the scope of the present disclosure.

Benefits, other advantages, and solutions to problems have beendescribed above with regard to specific embodiments. However, thebenefits, advantages, solutions to problems, and any feature(s) that maycause any benefit, advantage, or solution to occur or become morepronounced are not to be construed as a critical, required, or essentialfeature of any or all the claims. Moreover, the particular embodimentsdisclosed above are illustrative only, as the disclosed subject mattermay be modified and practiced in different but equivalent mannersapparent to those skilled in the art having the benefit of the teachingsherein. No limitations are intended to the details of construction ordesign herein shown, other than as described in the claims below. It istherefore evident that the particular embodiments disclosed above may bealtered or modified and all such variations are considered within thescope of the disclosed subject matter. Accordingly, the protectionsought herein is as set forth in the claims below.

What is claimed is:
 1. A near-eye display system, comprising: a displaypanel; and a beam steering assembly facing the display panel, the beamsteering assembly including a first birefringent plate configurable toreplicate a light ray incident on the beam steering assembly, whereinthe replicated light ray is laterally shifted relative to an opticalpath of the light ray incident on the beam steering assembly.
 2. Thenear-eye display system of claim 1, wherein: an in-plane symmetry axisof the first birefringent plate is tilted relative to the optical pathof the light ray incident on the beam steering assembly.
 3. The near-eyedisplay system of claim 1, further comprising: an actuator coupled tothe beam steering assembly, the actuator to change a tilt angle betweenthe beam steering assembly and the optical path of the light rayincident on the beam steering assembly.
 4. The near-eye display systemof claim 3, further comprising: a display controller coupled to thedisplay panel, the display controller to drive the display panel todisplay a sequence of images; and a beam steering controller coupled tothe actuator, the beam steering controller to instruct the actuator toimpart a different tilt angle between the beam steering assembly and theoptical path of the light ray incident on the beam steering assembly,wherein the different tilt angle changes a lateral shift for light raysreplicated by the beam steering assembly.
 5. The near-eye display systemof claim 4, wherein: the replicated light ray represents a same visualcontent as the light ray incident on the beam steering assembly so thateach of the sequence of images is perceived by a user as having aresolution of the display panel and having pixels with an apparent sizethat is larger than an actual size of the pixels of the display panel.6. The near-eye display system of claim 1, wherein: the beam steeringassembly comprises a stacked pair of birefringent plates including thefirst birefringent plate and a second birefringent plate, and furtherwherein each of the first and second birefringent plates replicatesincident light rays.
 7. The near-eye display system of claim 6, furthercomprising: a quarter wave plate positioned between the firstbirefringent plate and the second birefringent plate, wherein thequarter wave plate polarizes light rays output from the firstbirefringent plate prior to passing the polarized light rays to thesecond birefringent plate.
 8. The near-eye display system of claim 6,wherein: the beam steering assembly outputs at least four light rays foreach light ray incident on the beam steering assembly.
 9. In a near-eyedisplay system, a method comprising: positioning a beam steeringassembly, including a first birefringent plate, at a first tilt angle sothat the beam steering assembly is tilted relative to an optical path ofa light ray incident on the beam steering assembly; and replicating thelight ray incident on the beam steering assembly by passing the lightray through the first birefringent plate, wherein the replicated lightray is laterally shifted by a first distance, based on the first tiltangle, relative to the optical path of the light ray.
 10. The method ofclaim 9, further comprising: repositioning the beam steering assembly toa second tilt angle so that the beam steering assembly is tiltedrelative to the optical path of the light ray incident on the beamsteering assembly; and replicating the light ray incident on the beamsteering assembly by passing the light ray through the firstbirefringent plate, wherein the replicated light ray is laterallyshifted by a second distance, based on the second tilt angle, relativeto the optical path of the light ray.
 11. The method of claim 10,wherein: repositioning the beam steering assembly comprises controllingan actuator coupled to the beam steering assembly to change from thefirst tilt angle to the second tilt angle.
 12. The method of claim 9,further comprising: controlling a display panel facing the beam steeringassembly to display a first image while the beam steering assembly is afirst configuration state with the beam steering assembly positioned atthe first tilt angle; and controlling the beam steering assembly toimpart a first lateral shift for the first image.
 13. The method ofclaim 12, further comprising: controlling the display panel facing thebeam steering assembly to display a second image; and signaling the beamsteering assembly to enter a second configuration state with the beamsteering assembly positioned at a second tilt angle to impart a secondlateral shift for the second image.
 14. The method of claim 13, furthercomprising: controlling the display panel to display the first andsecond images within a visual perception interval so that the first andsecond images are perceptible as a single image with an effectiveresolution that is higher than a native resolution of the display panel.15. The method of claim 13, wherein: the first and second images containthe same visual content and which are displayed in a period of time lessthan a visual persistence interval so that the first and second imagesare perceptible as a single image having a resolution of the displaypanel and having pixels with an apparent size that is larger than anactual size of the pixels of the display panel.
 16. The method of claim9, wherein: the beam steering assembly includes the first birefringentplate and a second birefringent plate, and the first tilt angle of thebeam steering assembly replicates the light ray incident on the beamsteering assembly into a plurality of laterally shifted beams, andwherein each of the plurality of laterally shifted beams includes adifferent lateral shift.
 17. The method of claim 16, further comprising:passing the plurality of laterally shifted beams for display so that theplurality of laterally shifted beams are perceptible as a single imagehaving a resolution of a display panel facing the beam steering assemblyand having pixels with an apparent size that is larger than an actualsize of the pixels of the display panel.
 18. A rendering system,comprising: at least one processor; a beam steering assembly facing adisplay panel, the beam steering assembly including a first birefringentplate configurable to replicate a light ray incident on the beamsteering assembly, wherein the replicated light ray is laterally shiftedrelative to an optical path of the light ray incident on the beamsteering assembly; and a storage component to store a set of executableinstructions, the set of executable instructions configured tomanipulate the at least one processor to sample a source image to rendera first image including a first array of pixels, wherein the first arrayof pixels are laterally shifted relative to the optical path by the beamsteering assembly prior to presentation to a user.
 19. The renderingsystem of claim 18, wherein the set of executable instructions arefurther configured to manipulate the at least one processor to: resamplethe source image to render a second image comprising a second array ofpixels; and signal a display controller coupled to the display panel topresent both the first image and the second image in a period of timeless than a visual persistence interval so that the first array ofpixels and the second array of pixels are perceptible as a single image.20. The rendering system of claim 19, wherein the set of executableinstructions are further configured to manipulate the at least oneprocessor to: resample the source image to render a second imagecomprising a second array of pixels; and signal a display controllercoupled to the display panel to present both the first image and thesecond image in a period of time less than a visual persistence intervalso that the first and second array of pixels are perceptible as a singleimage.